Skip to main content
SpringerLink
Log in

Conjunctive Query Answering in Finitely-Valued Fuzzy Description Logics

  • Conference paper
Web Reasoning and Rule Systems (RR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8741))

Included in the following conference series:

Abstract

Fuzzy Description Logics (DLs) generalize crisp ones by providing membership degree semantics for concepts and roles. A popular technique for reasoning in fuzzy DL ontologies is by providing a reduction to crisp DLs and then employ reasoning in the crisp DL. In this paper we adopt this approach to solve conjunctive query (CQ) answering problems for fuzzy DLs. We give reductions for Gödel, and Łukasiewicz variants of fuzzy and two kinds of fuzzy CQs. The correctness of the proposed reduction is proved and its complexity is studied for different fuzzy variants of .

Partially supported by DFG SFB 912 (HAEC) and the Cluster of Excellence ‘cfAED’.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baader, F., Borgwardt, S., Peñaloza, R.: On the decidability status of fuzzy \(\mathcal{ALC}\) with general concept inclusions. Journal of Philosophical Logic (2014)

    Google Scholar 

  2. Bobillo, F., Delgado, M., Gómez-Romero, J.: Optimizing the Crisp Representation of the Fuzzy Description Logic \(\cal \mathcal{SROIQ}\). In: da Costa, P.C.G., d’Amato, C., Fanizzi, N., Laskey, K.B., Laskey, K.J., Lukasiewicz, T., Nickles, M., Pool, M. (eds.) URSW 2005 - 2007. LNCS (LNAI), vol. 5327, pp. 189–206. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Bobillo, F., Delgado, M., Gómez-Romero, J., Straccia, U.: Fuzzy Description Logics under Gödel semantics. International Journal of Approximate Reasoning 50(3), 494–514 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bobillo, F., Straccia, U.: Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic \(\mathcal{SROIQ}\). Information Sciences 181(4), 758–778 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bobillo, F., Straccia, U.: Finite fuzzy Description Logics and crisp representations. In: Bobillo, F., Costa, P.C.G., d’Amato, C., Fanizzi, N., Laskey, K.B., Laskey, K.J., Lukasiewicz, T., Nickles, M., Pool, M. (eds.) URSW 2008-2010/UniDL 2010. LNCS, vol. 7123, pp. 99–118. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Borgwardt, S., Peñaloza, R.: Consistency reasoning in lattice-based fuzzy Description Logics. International Journal of Approximate Reasoning (2013)

    Google Scholar 

  7. Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: Proceedings of the Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pp. 149–158. ACM (1998)

    Google Scholar 

  8. Cerami, M., Straccia, U.: On the (un)decidability of fuzzy Description Logics under Łukasiewicz t-norm. Information Sciences 227, 1–21 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  9. Cheng, J., Ma, Z.M., Zhang, F., Wang, X.: Deciding query entailment for fuzzy \(\mathcal{SHIN}\) ontologies. In: Gómez-Pérez, A., Yu, Y., Ding, Y. (eds.) ASWC 2009. LNCS, vol. 5926, pp. 120–134. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Cheng, J., Ma, Z.M., Zhang, F., Wang, X.: Deciding query entailment in fuzzy Description Logic knowledge bases. In: Bhowmick, S.S., Küng, J., Wagner, R. (eds.) DEXA 2009. LNCS, vol. 5690, pp. 830–837. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Cimiano, P., Haase, P., Ji, Q., Mailis, T., Stamou, G., Stoilos, G., Tran, D.T., Tzouvaras, V.: Reasoning with large A-Boxes in fuzzy Description Logics using DL reasoners: an experimental evaluation. In: Proceedings of the ESWC Workshop on Advancing Reasoning on the Web: Scalability and Commonsense (2008)

    Google Scholar 

  12. Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive query answering for the Description Logic \(\mathcal{SHIQ}\). Journal of Artificial Intelligence Research 31, 157–204 (2008)

    MATH  MathSciNet  Google Scholar 

  13. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: Proc. of the 10th International Conference of Knowledge Representation and Reasoning (KR 2006), vol. 6, pp. 57–67 (2006)

    Google Scholar 

  14. Kollia, I., Glimm, B.: Optimizing SPARQL query answering over OWL ontologies. Journal of Artificial Intelligence Research 48, 253–303 (2013)

    MATH  Google Scholar 

  15. Li, Y., Xu, B., Lu, J., Kang, D., Wang, P.: A family of extended fuzzy Description Logics. In: Computer Software and Applications Conference, vol. 1, pp. 221–226. IEEE (2005)

    Google Scholar 

  16. Mailis, T., Peñaloza, R., Turhan, A.Y.: Conjunctive query answering in finitely-valued fuzzy Description Logics. Tech. rep., Chair of Automata Theory, Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany (2014)

    Google Scholar 

  17. Mailis, T., Stoilos, G., Stamou, G.: Expressive reasoning with Horn rules and fuzzy Description Logics. Knowledge and Information Systems 25(1), 105–136 (2010)

    Article  Google Scholar 

  18. Ortiz, M., Rudolph, S., Šimkus, M.: Query answering in the Horn fragments of the description logics \(\mathcal{SHOIQ}\) and \(\mathcal{SROIQ}\). In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence, vol. 2, pp. 1039–1044. AAAI Press (2011)

    Google Scholar 

  19. Pan, J.Z., Stamou, G.B., Stoilos, G., Thomas, E.: Expressive querying over fuzzy DL-Lite ontologies. In: 20th International Workshop on Description Logics (2007)

    Google Scholar 

  20. Shearer, R., Motik, B., Horrocks, I.: Hermit: A highly-efficient OWL reasoner. In: Proc. of the 5th Int. Workshop on OWL: Experiences and Directions (OWLED), Karlsruhe, Germany (2008)

    Google Scholar 

  21. Simou, N., Stoilos, G., Tzouvaras, V., Stamou, G.B., Kollias, S.D.: Storing and querying fuzzy knowledge in the Semantic Web. In: 7th International Workshop on Uncertainty Reasoning For the Semantic Web, Karlsruhe, Germany (2008)

    Google Scholar 

  22. Stoilos, G., Stamou, G.B.: Extending fuzzy Description Logics for the Semantic Web. In: 3rd International Workshop of OWL: Experiences and Directions, Innsbruck (2007)

    Google Scholar 

  23. Straccia, U.: Transforming fuzzy Description Logics into classical Description Logics. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 385–399. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  24. Straccia, U.: Answering vague queries in fuzzy DL-Lite. In: Proceedings of the 11th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2006), pp. 2238–2245 (2006)

    Google Scholar 

  25. Straccia, U.: Towards top-k query answering in Description Logics: the case of DL-Lite. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 439–451. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  26. Straccia, U.: Foundations of Fuzzy Logic and Semantic Web Languages. CRC Press (2013)

    Google Scholar 

  27. Straccia, U.: On the top-k retrieval problem for ontology-based access to databases. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds.) ICCI 1991. LNCS, vol. 497, pp. 95–114. Springer, Heidelberg (1991)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chair for Automata Theory, Theoretical Computer Science, TU Dresden, Germany

    Theofilos Mailis, Rafael Peñaloza & Anni-Yasmin Turhan

  2. Center for Advancing Electronics Dresden, Germany

    Rafael Peñaloza

Authors
  1. Theofilos Mailis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rafael Peñaloza
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anni-Yasmin Turhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Information Systems, Birkbeck, University of London, Malet Street,, WC1E 7HX, London, UK

    Roman Kontchakov

  2. LIRMM, 161, rue ADA, Montpellier Cedex 5, 34395, France

    Marie-Laure Mugnier

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Mailis, T., Peñaloza, R., Turhan, AY. (2014). Conjunctive Query Answering in Finitely-Valued Fuzzy Description Logics. In: Kontchakov, R., Mugnier, ML. (eds) Web Reasoning and Rule Systems. RR 2014. Lecture Notes in Computer Science, vol 8741. Springer, Cham. https://doi.org/10.1007/978-3-319-11113-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11113-1_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11112-4

  • Online ISBN: 978-3-319-11113-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation